Stress and Hyperstress as Fundamental Concepts in Continuum Mechanics and in Relativistic Field Theory

TL;DR

This paper explores the fundamental concepts of stress and hyperstress from classical continuum mechanics and their relativistic counterparts, the energy-momentum and hypermomentum currents, highlighting their conservation laws and conditions for symmetry.

Contribution

It bridges classical continuum mechanics with relativistic field theory by translating stress concepts into spacetime currents and analyzing their conservation properties.

Findings

Hyperstress translates into hypermomentum current in spacetime.

Hypermomentum can be decomposed into spin, dilation, and shear components.

Conditions for symmetry of the momentum current are identified.

Abstract

The notions of stress and hyperstress are anchored in 3-dimensional continuum mechanics. Within the framework of the 4-dimensional spacetime continuum, stress and hyperstress translate into the energy-momentum and the hypermomentum current, respectively. These currents describe the inertial properties of classical matter fields in relativistic field theory. The hypermomentum current can be split into spin, dilation, and shear current. We discuss the conservation laws of momentum and hypermomentum and point out under which conditions the momentum current becomes symmetric.